CBSE Class 6 Mathematics Revision Worksheet Set 13

Order of Operations (A)

Perform the operations in the correct order.

Question 1. \(7 \div (10 + 3 - 6)\)
Answer: First, evaluate inside the parentheses using the order of operations from left to right:
\(10 + 3 = 13\)
\(13 - 6 = 7\)
Now substitute back into the expression:
\(7 \div 7 = 1\)
In simple words: Solve inside the brackets first, then divide.

Exam Tip: Always follow the BODMAS rule: Brackets first, followed by Division, Multiplication, Addition, and Subtraction.

Question 2. \(9 \div 9 \times (8 + 7)\)
Answer: First, solve inside the parentheses:
\(8 + 7 = 15\)
Substitute back into the expression:
\(9 \div 9 \times 15\)
Next, perform division and multiplication from left to right:
\(9 \div 9 = 1\)
\(1 \times 15 = 15\)
In simple words: Simplify the brackets first, then calculate from left to right.

Exam Tip: When an expression has both multiplication and division of equal priority, always evaluate them strictly from left to right.

Question 3. \(4 \div (8 - 6) \div 2\)
Answer: First, evaluate inside the parentheses:
\(8 - 6 = 2\)
Substitute back into the expression:
\(4 \div 2 \div 2\)
Perform division from left to right:
\(4 \div 2 = 2\)
\(2 \div 2 = 1\)
In simple words: Solve the parentheses first, then divide step by step from left to right.

Exam Tip: Do not divide from right to left; always proceed from left to right for continuous division.

Question 4. \(10 \div 5 \times 3 \times 3\)
Answer: Perform division and multiplication from left to right:
\(10 \div 5 = 2\)
\(2 \times 3 = 6\)
\(6 \times 3 = 18\)
In simple words: Multiply and divide in order from left to right.

Exam Tip: Multiplication does not take precedence over division; they have equal rank and are evaluated from left to right.

Question 5. \(10 + 8 \div 1 - 5\)
Answer: Perform division first according to the order of operations:
\(8 \div 1 = 8\)
Substitute back into the expression:
\(10 + 8 - 5\)
Now perform addition and subtraction from left to right:
\(10 + 8 = 18\)
\(18 - 5 = 13\)
In simple words: Do the division before doing addition and subtraction.

Exam Tip: Division must always be completed before addition or subtraction.

Question 6. \((4 + 1 + 4) \div 3\)
Answer: First, evaluate inside the parentheses:
\(4 + 1 = 5\)
\(5 + 4 = 9\)
Substitute back into the expression:
\(9 \div 3 = 3\)
In simple words: Add all the numbers inside the brackets first, then divide by 3.

Exam Tip: Always resolve the entire contents of a bracket to a single number before applying outside operations.

Question 7. \(1 \times 2 \times (4 - 2)\)
Answer: First, evaluate inside the parentheses:
\(4 - 2 = 2\)
Substitute back into the expression:
\(1 \times 2 \times 2\)
Perform multiplication from left to right:
\(1 \times 2 = 2\)
\(2 \times 2 = 4\)
In simple words: Subtract inside the brackets first, then multiply.

Exam Tip: Parentheses always take the highest priority in the order of operations.

Question 8. \((10 - (10 - 8)) \times 2\)
Answer: First, evaluate the innermost parentheses:
\(10 - 8 = 2\)
Substitute this back into the outer parentheses:
\((10 - 2) \times 2\)
Evaluate the outer parentheses:
\(10 - 2 = 8\)
Multiply by 2:
\(8 \times 2 = 16\)
In simple words: Solve the inner brackets first, then the outer brackets, and finally multiply.

Question 9. \(10 + 9 \div (3 \times 3)\)
Answer: First, evaluate inside the parentheses:
\(3 \times 3 = 9\)
Substitute back into the expression:
\(10 + 9 \div 9\)
Perform the division next:
\(9 \div 9 = 1\)
Perform the addition last:
\(10 + 1 = 11\)
In simple words: Simplify the brackets, do the division, and finish with addition.

Exam Tip: Division is performed before addition.

Question 10. \(10 \div ((1 + 5) \div 6)\)
Answer: First, evaluate the innermost parentheses:
\(1 + 5 = 6\)
Substitute this into the expression:
\(10 \div (6 \div 6)\)
Evaluate the outer parentheses:
\(6 \div 6 = 1\)
Perform the final division:
\(10 \div 1 = 10\)
In simple words: Solve the inner brackets, then the outer brackets, and divide.

Exam Tip: Handle multiple layers of parentheses carefully from the inside out.

Question 11. \(5 + 4 - 3 + 9\)
Answer: Perform addition and subtraction from left to right:
\(5 + 4 = 9\)
\(9 - 3 = 6\)
\(6 + 9 = 15\)
In simple words: Calculate step by step from left to right.

Exam Tip: Addition and subtraction have equal priority, so always evaluate them strictly from left to right.

Question 12. \(4 + 1 + 6 - 4\)
Answer: Perform addition and subtraction from left to right:
\(4 + 1 = 5\)
\(5 + 6 = 11\)
\(11 - 4 = 7\)
In simple words: Add and subtract in order from left to right.

Exam Tip: Proceed sequentially from left to right for operations of the same precedence.

Question 13. \(2 \times 2 \div (10 - 9)\)
Answer: First, evaluate inside the parentheses:
\(10 - 9 = 1\)
Substitute back into the expression:
\(2 \times 2 \div 1\)
Perform multiplication and division from left to right:
\(2 \times 2 = 4\)
\(4 \div 1 = 4\)
In simple words: Solve the brackets first, then multiply and divide from left to right.

Exam Tip: Always clear brackets before performing multiplication or division.

Question 14. \(8 + 3 \div 1 + 9\)
Answer: Perform the division first:
\(3 \div 1 = 3\)
Substitute back into the expression:
\(8 + 3 + 9\)
Now perform addition from left to right:
\(8 + 3 = 11\)
\(11 + 9 = 20\)
In simple words: Divide first, then add the numbers together.

Exam Tip: Division takes precedence over addition.

Question 15. \(10 \div (4 - 2) \div 1\)
Answer: First, evaluate inside the parentheses:
\(4 - 2 = 2\)
Substitute back into the expression:
\(10 \div 2 \div 1\)
Perform division from left to right:
\(10 \div 2 = 5\)
\(5 \div 1 = 5\)
In simple words: Solve inside the brackets first, then divide from left to right.

Exam Tip: Continuous division must always be evaluated strictly from left to right.